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Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions

Davidchack, R.L.; Ouldridge, T.E.; Tretyakov, M.V.

Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions Thumbnail


Authors

R.L. Davidchack

T.E. Ouldridge



Abstract

We introduce new Langevin-type equations describing the rotational and translational motion of rigid bodies interacting through conservative and non-conservative forces, and hydrodynamic coupling. In the absence of non-conservative forces the Langevin-type equations sample from the canonical ensemble. The rotational degrees of freedom are described using quaternions, the lengths of which are exactly preserved by the stochastic dynamics. For the proposed Langevin-type equations, we construct a weak 2nd order geometric integrator which preserves the main geometric features of the continuous dynamics. The integrator uses Verlet-type splitting for the deterministic part of Langevin equations appropriately combined with an exactly integrated Ornstein-Uhlenbeck process. Numerical experiments are presented to illustrate both the new Langevin model and the numerical method for it, as well as to demonstrate how inertia and the coupling of rotational and translational motion can introduce qualitatively distinct behaviours.

Journal Article Type Article
Acceptance Date Nov 26, 2017
Online Publication Date Dec 12, 2017
Deposit Date Dec 13, 2017
Publicly Available Date Dec 13, 2017
Journal Journal of Chemical Physics
Print ISSN 0021-9606
Electronic ISSN 1089-7690
Publisher American Institute of Physics
Peer Reviewed Peer Reviewed
Volume 147
Issue 22
Article Number 224103
DOI https://doi.org/10.1063/1.4999771
Keywords rigid body dynamics; quaternions; hydrodynamic interactions; Stokesian dynamics; canonical
ensemble; Langevin equations; stochastic differential equations; weak approximation; ergodic limits; stochastic
geometric integrators
Public URL https://nottingham-repository.worktribe.com/output/899501
Publisher URL http://aip.scitation.org/doi/full/10.1063/1.4999771

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